Correcting Predictions for Approximate Bayesian Inference
This addresses the issue of inaccurate decision-making in downstream applications for practitioners using approximate Bayesian inference, though it appears incremental as it builds on existing Bayesian modeling frameworks.
The paper tackles the problem of sub-optimal decisions caused by approximate Bayesian inference methods, presenting a novel approach that corrects predictions by training a separate model to optimize decisions under the approximate posterior, applicable as a plug-in module for arbitrary probabilistic programs.
Bayesian models quantify uncertainty and facilitate optimal decision-making in downstream applications. For most models, however, practitioners are forced to use approximate inference techniques that lead to sub-optimal decisions due to incorrect posterior predictive distributions. We present a novel approach that corrects for inaccuracies in posterior inference by altering the decision-making process. We train a separate model to make optimal decisions under the approximate posterior, combining interpretable Bayesian modeling with optimization of direct predictive accuracy in a principled fashion. The solution is generally applicable as a plug-in module for predictive decision-making for arbitrary probabilistic programs, irrespective of the posterior inference strategy. We demonstrate the approach empirically in several problems, confirming its potential.